Solvation, Solute Rotation and Vibration Relaxation, and Electron

Aug 18, 2007 - She received her Ph.D. degree in physics from Seoul National University in 2005. She is currently a postdoctoral research associate in ...
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Acc. Chem. Res. 2007, 40, 1130–1137

Solvation, Solute Rotation and Vibration Relaxation, and Electron-Transfer Reactions in Room-Temperature Ionic Liquids YOUNGSEON SHIM,† DAUN JEONG,‡ SWATI MANJARI,† MOO YOUNG CHOI,‡,§ AND HYUNG J. KIM*,†,| Department of Chemistry, Carnegie Mellon University, Pittsburgh, Pennsylvania 15213, Department of Physics and Astronomy, Seoul National University, Seoul 151-747, Korea, School of Physics, Korea Institute for Advanced Study, Seoul 130-722, Korea, and Department of Physics, Korea University, Seoul 136-701, Korea Received March 13, 2007 ABSTRACT A brief account of recent simulation and theoretical model studies of various solution-phase processes in room-temperature ionic liquids is given. These include structure and dynamics of equilibrium and nonequilibrium solvation, solute rotation and vibrational energy relaxation, and free energetics and dynamics of unimolecular electron-transfer reactions. Special attention is paid to both the aspects shared by and the contrasts with polar solvents under normal conditions. A brief comparison with available experiments is also made.

1. Introduction Recently, ionic liquids based on bulky and asymmetric cations, e.g., N,N′-dialkylimidazolium and N-alkylpyridinium, paired with a variety of different anions have been the subject of intensive study because of their exciting potential as a “green” alternative to toxic organic solvents and a wide range of materials and device applications.1 This class of systems exists as a liquid at or near room temperature; hence, they are often referred to as roomYoungseon Shim was born in Incheon, Korea, in 1977. She received her Ph.D. degree in physics from Seoul National University in 2005. She is currently a postdoctoral research associate in the Department of Chemistry at Carnegie Mellon University. Her research interest is the computational study of solvation and chemical reactions in ionic liquids and polar solvents. Daun Jeong was born in Jeongeup, Korea, in 1979. She completed her doctorate degree in physics at Seoul National University in 2007. She currently holds a postdoctral position in the Chemistry Department at Seoul National University. Her research focus is the dynamics of ionic liquids and self-assembled peptide amphiphiles. Swati R. Manjari was born in Delhi, India, in 1976. She completed her Ph.D. degree in chemistry at Carnegie Mellon University in 2006. She is currently studying solvation dynamics in bulk and confined room-temperature ionic liquids using molecular simulations as a postdoctoral researcher in the Department of Chemistry at Carnegie Mellon University. Moo Young Choi was born in Seoul, Korea, in 1957. After he received his Ph.D. degree in physics from Stanford University in 1984, he worked at Ohio State University as a postdoctoral researcher. Since 1987, he has been on the faculty of Seoul National University, where he is currently a Professor of Physics. He also holds a position of Affiliated Professor at Korea Institute for Advanced Study. His research interest spans phase transitions and dynamics of complex systems, physics of biological systems, and mesoscopic quantum phenomena. 1130

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temperature ionic liquids (RTILs). RTILs are usually nonvolatile, nonflammable, and thermally stable. Therefore, volatile products of chemical synthesis can be separated completely through distillation, and RTILs can be recycled. This helps to reduce toxic wastes significantly. Because of their high intrinsic conductivity and wide electrochemical window as well as nonvolatility, RTILs also provide an excellent candidate for an electrolyte in electrochemical devices, such as batteries and solar cells. The last few years have seen significant progress in unraveling important details of physicochemical properties of RTILs, thanks to extensive experimental and theoretical studies. For differing aspects of these efforts, the reader is referred to many excellent Accounts in this issue of Accounts of Chemical Research. Our own efforts have been focussed mainly on gaining a fundamental understanding of solvation and related processes in RTILs at the microscopic level via molecular dynamics (MD) computer simulations and theoretical modeling. These include structure and dynamics of equilibrium and nonequilibrium solvation,2–5 rotational6 and vibrational energy7 relaxation, and chemical reactions involving charge shift and transfer.8 In this Account, we present a brief overview of these studies and elucidate similarities and differences between polar solvents and RTILs. We give only certain highlights of our results. For details, the reader is referred to the original works.2–8 The outline of this Account is as follows: In section 2, a brief explanation of models and methods employed in our study of 1-ethyl-3-methylimidazolium hexafluorophosphate (EMI+PF6-) is given. Solvation structure and dynamics in EMI+PF6- are analyzed in section 3. Effective polarity is also considered there. We examine solute rotational dynamics and related dynamic heterogeneity in EMI+PF6- in section 4 and vibrational energy relaxation in section 5. Free energetics and dynamics of unimolecular electron transfer are considered in section 6. Section 7 concludes this Account.

2. Models and Methods We begin with a brief description of models employed in our MD simulations. We use a simple diatomic solute as a probe for solvation and related processes in EMI+PF6-. * To whom correspondence should [email protected]. † Carnegie Mellon University. ‡ Seoul National University. § Korea Institute for Advanced Study. | Korea University.

be

addressed.

E-mail:

Hyung J. Kim was born in Seoul, Korea, in 1956. After he completed his graduate research in chemical physics at the State University of New York (SUNY) at Stony Brook in 1988, he did postdoctoral research in the Department of Chemistry and Biochemistry at the University of Colorado, Boulder, CO. In 1992, he joined the faculty of Carnegie Mellon University, where he is currently a Professor of Chemistry. He is also an adjunct faculty member of the Department of Physics, Korea University. His research theme centers around equilibrium and nonequilibrium statistical mechanics of solution systems and chemical reaction dynamics in condensed phases. 10.1021/ar700061r CCC: $37.00

 2007 American Chemical Society Published on Web 08/18/2007

Various Solution-Phase Processes in RTILs Shim et al.

FIGURE 1. EMI+ ion. Two constituent solute atoms, separated by 3.5 Å, are identical except for their charge assignments q. Three different charge distributions are considered: a neutral pair (NP) with no charges, an ion pair (IP) with q ) (e, and their intermediate state (HIP) with q ) (0.5e, where e is the elementary charge. We describe solute electronic structure variations needed in the analysis of solvation and electron transfer using two nonpolarizable electronic states a and b that are degenerate in energy (a,b ) NP,IP). For a given solvent configuration Q and a solute electronic state i ()a,b), the total energy of the solute–solvent system is denoted as Ei(Q). The Franck–Condon (FC) energy ∆Eafb(Q) associated with the a f b transition

∆Eafb(Q) ) Eb(Q) - Ea(Q)

(1)

measures the difference in the solvent-induced stabilization of states a and b, which varies with Q. Thus, ∆Eafb is widely employed to describe the collective influence of the solvent on the solute. The average FC energy

〈∆Eafb 〉 )

∫ dQf eqa (Q)∆Eafb(Q)

(2)

determined with equilibrium ensemble distribution f eq a (Q) in the presence of the a-state solute describes the solvation-stabilization difference between a and b associated with the steady-state a f b transition. All simulations in EMI+PF6- were conducted in the canonical ensemble at temperature T ) 400 K using the DL_POLY program.9 A united-atom representation was employed for CH2 and CH3 moieties of EMI+ (Figure 1) as well as for PF6-. For a comparison, we also simulated acetonitrile and water systems at room temperature using the model descriptions of refs 10 and 11, respectively. For details of the simulations and potential models, the reader is referred to refs .2–8

3. Solvation Structure and Dynamics Solute–solvent electrostatic interactions play a central role in solvation in polar solvents. These interactions induce the reorientation of solvent dipoles (“polarization”) and enhance local solvent density (“electrostriction”) around a polar solute, compared to a nonpolar solute (see Figure 2 below). This reorganization of solvent molecules is fundamental to, e.g., charge-transfer reactions and related spectroscopies in solution. RTILs are another solvent class where the solute–solvent electrostatic interactions can be

FIGURE 2. Solvent radial distribution functions around the solute. Distributions of anions and centers of cations in EMI+PF6- around, respectively, the (a) positively and (b) negatively charged sites of IP (—), HIP (- · -), and a neutral site of NP (- - -) are shown. g(r) of N and central C of acetonitrile around the solute (+) and (-) sites are presented in c and d, respectively. In b, the cation center is defined as the midpoint of two N atoms of the imidazole ring of EMI+ (Figure 1). of primary importance. To obtain a molecular-level understanding of the roles played by these interactions in RTILs, we first investigate the structure and dynamics of solvation in EMI+PF6- and their variations with solute electronic structure. Structure and Effective Polarity. Radial distribution functions g(r) of anions and cations around, respectively, the positively and negatively charged sites of diatomic solutes in EMI+PF6- are exhibited in Figure 2. For a comparison, g(r) of the nitrogen atom with a partial negative charge and g(r) of the central carbon atom with a partial positive charge of solvent molecules in acetonitrile are also shown. There is pronounced structuremaking in both solvents as the solute charge separation increases. Solvent anions (cations) in EMI+PF6- are brought in closer to the positive (negative) site of the solute, and their local density grows as the solute dipole moment increases (“electrostriction”).2,3,8,12 Similar trends are obtained in acetonitrile. Although not presented here, anisotropy in the angular distributions of solvent ions around the solute increases markedly as its charge distribution changes from NP to IP in RTILs.3 We thus expect that charge shift and transfer processes in RTILs will be accompanied by significant reorganization of solvent ions, analogous to polar solvents. It is worthwhile to note that the overall extent of solvation structure variations is more pronounced in EMI+PF6- than in acetonitrile. For instance, g(r) for the central carbon of acetonitrile (Figure 2d), located close to the molecular center of mass, does not vary much with the solute charge distribution despite its partial positive charge, while g(r) for centers of anions VOL. 40, NO. 11, 2007 / ACCOUNTS OF CHEMICAL RESEARCH

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Various Solution-Phase Processes in RTILs Shim et al.

FIGURE 3. Local charge density Q(r) around various sites of the (a) solute and (b) solvent in EMI+PF6-. Table 1. Simulation Resultsa solvent

T (K)

density

〈∆ENPfIP〉

EMI+ClEMI+PF6EMI+PF6CH3CN water

400 400 400 300 298

1.1 1.31 1.375 0.73 0.998

100.6 83.8 94.1 76.5 121.2

a

Units: g/cm3 (density) and kcal/mol (energy).

(Figure 2a) and cations (Figure 2b) in EMI+PF6- show marked structural enhancement as the solute dipole grows.8 A likely reason is that EMI+ and PF6- can be displaced independent of each other as long as the overall electroneutrality condition is met, whereas the positively and negatively charged sites of an acetonitrile molecule cannot. Figure 3a shows the local charge densities Q(r) around the solute in EMI+PF6-. While Q(r) ) 0 nearly everywhere around NP, the cation-rich/anion-deficient and anionrich/cation-deficient regions alternate around IP. Thus, in addition to electrostriction, solute–solvent electrostatic interactions result in the (smeared-out) separation of cations and anions in RTILs, while they lead to the reorientation of solvent dipoles in polar solvents. The overall amplitudes of Q(r) diminish as the distance r from IP increases. The peak positions of Q(r) generally agree with those of corresponding g(r) in Figure 2. To gain further insight, we analyze our results via

2πr A +φ Q(r) ) e-r⁄λsin r d

(

)

(3)

originally developed for strongly coupled simple ionic systems.13 Here, λ is the screening length, and d and φ are the period and phase associated with charge oscillations, respectively. We estimate λ ∼ 10 and d ∼ 6 Å for Q(r) around IP. For charge densities around solvent ions (Figure 3b), eq 3 yields λ ≈ 10 Å for various sites of EMI+ and ∼20 Å for PF6-. Similar results were obtained for other RTILs.3,14 Because of the large size of solvent ions, the screening length in RTILs is rather long. We turn to effective polarity, which gauges the power of solvents of solvating polar solutes. Experimentally, the effective polarity is often measured as solvent-induced shifts of absorption spectra of polar chromophores, e.g., ET(30) and Kosower Z factors.15 Empirical polarity scales thus obtained are very similar to 〈∆EIPfNP〉 in eq 2. The results in Table 1 indicate that, insofar as their solvating capabilities are concerned, RTILs behave as a more polar 1132

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FIGURE 4. (a) Dynamic Stokes shift Safb(t) and (b) contributions from solvent rotational and translational motions to ∆ENPfIP(t) in EMI+PF6- (∆∆Eafb(t) ≡ ∆Eafb(t) – ∆Eafb(0)). ∆EIPfNP(t) (not presented here) shows a very similar behavior. solvent than acetonitrile, consonant with solvatochromic measurements.16 Although their dielectric constants are not high (ε ≈ 10),17,18 the monopolar charge character of constituent ions of RTILs allows strong electrostatic interactions with and thus leads to substantial solvation stabilization of solute charge distributions. Nonetheless, they are not as polar as water. Dynamics. The normalized dynamic Stokes shift

Safb(t) )

∆Eafb(t) - ∆Eafb(∞) ∆Eafb(0) - ∆Eafb(∞)

(4)

is widely used to describe solvation dynamics. In eq 4, ∆Eafb(t) is the average FC energy associated with a f b at time t after an instantaneous change in the solute electronic structure from the charge distribution of b to that of a and the average is over the initial distribution of solvent configurations in equilibrium with the b-state solute. MD results in Figure 4a show that Safb(t) is characterized by at least two vastly different dynamics, ultrafast subpicosecond relaxation and extremely slow nonexponential decay.4,5 The former is attributed mainly to small-amplitude inertial translations of ions (see below), and the latter is attributed to ion transport via diffusion.2,4 Perhaps, the most notable aspect of Figure 4a is the prominent role of the ultrafast dynamics. Despite its relatively high viscosity, more than 60% of the entire Safb(t) relaxation in EMI+PF6- occurs via ultrafast dynamics in the first ∼0.5 ps! Other related RTILs show similar behavior.4,19 This state of affairs is generally in good agreement with time-resolved spectroscopy measurements.20–26 To understand molecular motions responsible for Safb(t), we consider respective contributions of solvent translations and rotations to ∆Eafb(t). Figure 4b shows that translation dynamics account for almost 90% of the overall solvent relaxation.4 Thus, ion translations play a dominant role in solvation dynamics in RTILs in contrast to molecular rotations in polar solvents under normal conditions. We proceed to solvent structural relaxation4 in Figure 5, where time evolution of anion radial distributions around the solute (+) site subsequent to solute FC transitions is shown. In Figure 5a, the solvent, initially equilibrated to the IP solute, relaxes to a new state in equilibrium with NP. In the first ∼0.2 ps, there are hardly any changes in the

Various Solution-Phase Processes in RTILs Shim et al.

FIGURE 5. Relaxation of radial distributions of PF6- subsequent to instantaneous changes in the solute charge distribution in EMI+PF6-. Distributions in a and b represent structural relaxation accompanying SNPfIP(t) and SIPfNP(t), respectively. solvation structure. The only noticeable change is in the first solvation shell, the peak of which shifts from r ≈ 4.4 to 4.6 Å. According to Figure 4a, however, this very minor structural change accounts for ∼50% of SNPfIP(t) relaxation. The corresponding change in energy is ∼30 kcal/mol (Figure 4b). To understand this, we consider the anion coordination number nA, defined as the number of PF6- located within 6 Å from the solute (+) site. At t ) 0, the anion coordination number is nA ) 4.3. If we assume that the average separation between the solute (+) site and PF6- in its first solvation shell increases from 4.4 to 4.6 Å during the first 0.2 ps, then the magnitude of their electrostatic interaction energy decreases by ∼14 kcal/mol. Thus, the anions in the first solvation shell alone can account for nearly 50% of the energy relaxation during ∼0.2 ps. This indicates that shorttime relaxation of SNPfIP(t) arises predominantly from motions of a few ions close to the solute and thus does not provide an accurate measure for solvation structure changes.4 The overall trend in Figure 5b is similar to that in Figure 5a. Structural changes in the first ∼0.2 ps are nearly insignificant, while corresponding relxation in SIPfNP(t) is very substantial. This again shows that the ultrafast component of dynamic Stokes shifts is not a proper indicator of accompanying solvation structure changes. Despite their similarities, however, there is one important difference between the two cases of Figure 5. Because initial ion coordination numbers are low, e.g., nA ) 2.8, in Figure 5b (cf. nA ) 4.3 in Figure 5a), the ions close to the solute alone are not sufficient to account for the ultrafast energy relaxation of a large magnitude associated with SIPfNP(t). Thus, ions in regions located farther from the solute than its first solvation shell play a more significant role in the subpicosecond relaxation of SIPfNP(t) than the SNPfIP(t) case.4 We turn to equilibrium solvation dynamics.2,3,5,19,27–29 MD results for the normalized time correlation function (TCF)

Cafb(t) ≡

〈δ∆Eafb(0)δ∆Eafb(t)〉 〈(δ∆Eafb)2 〉 δ∆Eafb(t) ) ∆Eafb(t) - 〈∆Eafb 〉(5)

in Figure 6a show that characteristics of Cafb(t) are very close to those of Safb(t), including two distinct dynamic regimes, the importance of ultrafast relaxation and the

FIGURE 6. (a) Cafb(t) in EMI+PF6-. (b) Solute polarizability effect on SIPfNP(t) (R ) solute polarizability along its molecular axis).

FIGURE 7. (a) Cl(t) for NP and NP5.5 in EMI+PF6-. (b) G(θ;t*) (t* ≡ t/τR(2)) for NP in EMI+PF6- and in acetonitrile. nonexponential behavior of long-time decay. Also noteworthy is that the long-time relaxation of Cafb(t) is reasonably described as a stretched exponential function.2,4 Its implications will be considered in section 4 below. Finally, we consider the effect of solute polarizability on solvation dynamics.5 According to MD results in Figure 6b, qualitative aspects of Safb(t) remain unaffected with the inclusion of the a-state polarizability. Quantitatively, increasing the a-state polarizability tends to reduce the contribution of ultrafast solvation dynamics to Safb(t). Similar results are obtained for Cafb(t). This generally yields a better agreement with experiments.26 This trend of solvation dynamics with solute polarizability was first found in the MD study of water.30

4. Rotational Dynamics In this section, we examine solute rotational dynamics in EMI+PF6- via TCFs Cl(t) and correlation time τR(l)

Cl(t) ) 〈 Pl[cosθ(t)] 〉

τ(l) R )

∫ ∞0 dtCl(t)

(6)

where Pl is the lth order Legendre polynomial and θ(t) is the angle between the solute molecular axis at time t and its initial direction. Figure 7a displays MD results on Cl(t) for NP.6 Its reorientational TCFs show a bimodal character, viz., relatively fast relaxation for t j 1 ps, followed by slow decay. The long-time relaxation shows a stretched exponential behavior exp[-(t/τl)βl] for 2 ps j t j 1 ns (β1 ) 0.54, τ1 ) 32 ps, and β2 ) 0.27, τ2 ) 12 ps). This is in line with polarization anisotropy decay measurements.23,31 The stretched exponential behavior, also observed in Cafb(t) above, is suggestive of dynamic heterogeneity (see below).32 Perhaps most striking is that the long-time decay of C2(t) is slower than that of C1(t), whereas the opposite VOL. 40, NO. 11, 2007 / ACCOUNTS OF CHEMICAL RESEARCH

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Various Solution-Phase Processes in RTILs Shim et al.

FIGURE 8. θ(t) for NP in EMI+PF6- for different 1 ns segments of the MD trajectory.6 trend results at short times. As a consequence, C1(t) and C2(t) intersect at t ≈ 60 ps. Their correlation times are τR(1) ≈ 50 and τR(2) ≈ 100 ps, i.e., τR(1) < τR(2). This reveals that NP rotations in EMI+PF6- do not fall in the regular diffusion regime (see below). To investigate the solute size effect on rotational dynamics, we studied another nonpolar diatomic solute (NP5.5) with a bond length of 5.5 Å. Its mass is adjusted, so that its moment of inertia is the same as that of NP with a bond length of 3.5 Å. Cl(t) of the bigger NP5.5 in the inset of Figure 7 shows more diffusion-like character than those of the smaller NP. For example, Cl(t) of NP5.5 relaxes faster as l increases; thus, no crossing is observed. Reorientations of NP5.5, although nonexponential, are closer to a single exponential than those of NP. This is another indirect evidence for dynamic heterogeneity in RTILs. Because of different length scales associated with locally heterogeneous environments, the range of heterogeneity accessible via a probe solute and its influence on rotational dynamics diminish as the solute size grows.32 A similar dependence of Cl(t) on the probe size was observed experimentally in RTILs.23 For a better understanding of Cl(t), we consider conditional probability

G(θ; t) ) 〈 δ(θ(t) - θ) 〉 )

∑ 2l 2+ 1 Pl(cosθ)sinθCl(t) l

FIGURE 9. (a) Svib(t) of NP and IP in EMI+PF6-. (b) Comparison of VER of IP in EMI+PF6- at 400 K and in acetonitrile and water at 298 K (υ ) 16). Subtrajectory 3 depicts extremely slow rotation; the solute is nearly frozen at θ ≈ 40° for more that 600 ps. In contrast, the solute in 4 undergoes frequent rotations of large amplitude. The marked diversity in characteristics of these long subtrajectories indicates that NP rotations in RTILs are hardly homogeneous. It suggests heterogeneous dynamics,32 some evidence of which was also observed in other simulations14,33–35 and experiments.25,36,37 Nevertheless, in view of the crossing of C1(t) and C2(t), the prevalent notion that single-exponential relaxation results in a given local environment and superposition of many different exponentials leads to a stretched exponential behavior does not apply to solute rotational dynamics in RTILs.6

5. Vibrational Energy Relaxation As another illustration of importance of solvent influence on solute dynamics, we consider vibrational energy relaxation (VER). We employ flexible diatomic solutes with a Morse potential

V(r) ) D[e-γ(r-r0) - 1]2

(7) associated with solute reorientation. We notice in Figure 7b that the main peak of G(θ; t) near θ ) 20° hardly moves, while its amplitude decreases with t. Thus, on average, solute molecules are trapped in this orientation for a long time. Another pronounced feature is that G(θ; t) develops a shoulder structure around θ ) 160°. (A similar structure was observed in reorientations of solvent ions in RTILs.)33,34 In contrast, solute rotations in acetonitrile (inset) do not show this structure. Because the shoulder structure becomes stronger with t, the probability of finding NP at large θ becomes enhanced in EMI+PF6- compared with the normal solvents, especially at long times. The enhanced probability for θ > 90° tends to decrease Cl(t) for odd l and thus accelerate its relaxation at later times because cos θ < 0. Cl(t) with even l on the other hand is insensitive to the sign of cos θ, so that the probability enhancement at large θ does not accelerate their longtime relaxation. This differing influence of probability enhancement at large θ is responsible for the crossing of C1(t) and C2(t) in Figure 7a. For further insight, four different 1 ns segments of the 60 ns equilibrium trajectory for NP rotations are presented in Figure 8. Subtrajectories 1 and 2 represent, respectively, fast and slow dynamics close to rotational diffusion. 1134

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µω20 ) 2Dγ2

(

Eυ ) pω0 υ +

1 2

) [1 - 4D (υ + 21 )](8) pω0

to compute the normalized VER function Svib(t) and average relaxation time T1

Svib(t) )

Evib(t) - Evib(∞) Evib(0) - Evib(∞)

T1 )

∫0∞ dtSvib(t)

(9)

where Evib(t) is the average vibrational energy at time t after the initial exciation of the solute from its ground to excited vibrational state with quantum number υ. In eq 8, µ and r are the solute-reduced mass and bond length, ω0 is the frequency at the minimum of V(r) and Eυ is the vibrational energy eigenvalue. In the simulations, the zeropoint energy was neglected and µ ) 7.5 amu, D )100 kcal/ mol, and γ ) 1.0735 Å–1 were employed, so that ω0 ) 600 cm-1. Results for Svib(t) in EMI+PF6- are presented in Figure 9a. One of the salient features is that VER of IP is much faster than that of NP. For the υ ) 16 initial state, T1 is ∼51 ps for NP, while it is much shorter (3.2 ps) for IP. For υ ) 61, T1 ≈ 14 and 1.0 ps, respectively. Similar trends were found previously in normal polar solvents.38 The acceleration of VER with an increasing solute charge

Various Solution-Phase Processes in RTILs Shim et al.

ably larger than that in acetonitrile. This is probably closely related to huge electrostrictive effects in the former observed in Figure 2 above. Figure 10b displays variations of the ET barrier height ∆Fq with the free energy of the reaction ∆Frxn in EMI+PF6-. For a comparison, the Marcus theory48 predictions

(∆Frxn + λav)2 ∆F ) 4λav q

+

PF6-

FIGURE 10. (a) Diabatic free-energy curves for CS/CR in EMI at 400 K and CH3CN at 298 K. The IP curve is shifted, so that the reaction is thermoneutral. (b) ∆Fq versus ∆Frxn in EMI+PF6-. separation is usually attributed to electrostriction.7,39,40 The solvent density enhancement near the solute with an increasing solute dipole (cf. Figure 2) strengthens the short-range solute–solvent interactions and, as a consequence, enhances spatial variations of the force and thus friction on the solute vibrations exerted by the solvent. Another noteworthy feature is that T1 varies with the initial excitation energy; VER from the υ ) 61 state is faster than that from υ ) 16, by a factor of ∼3 for both the IP and NP solutes. This mainly arises from the increase in vibrational amplitudes with growing υ, which in turn enhances the variations of the solvent force on the solute bond and thus accelerates VER.7 In Figure 9b, VER in EMI+PF6- is compared with that in water and acetonitrile.7 Basic qualitative aspects of VER are similar among three solvents, including the acceleration of VER (results not shown here) with an increasing solute dipole and growing initial υ. Quantitatively, T1 in EMI+PF6- is close to that in acetonitrile, while water shows much faster VER. This is in good accordance with recent measurements with small anionic solutes.41

6. Electron-Transfer Reaction We now turn to electron-transfer (ET) reactions42–46 in EMI+PF6-, in particular, unimolecular charge separation and recombination (CS/CR) processes NP h IP. ET Free Energetics. The diabatic free-energy curves for the NP and IP states in EMI+PF6- and acetonitrile determined with the free-energy perturbation method47 along ∆ENPfIP are compared in Figure 10a.8 Overall characteristics of the NP and IP curves are similar between the two solvents. While both curves are anharmonic, their anharmonicity is not that strong for -40 j ∆ENPfIP j 40 kcal/mol. We also observe that the NP curve is wider than IP, especially in EMI+PF6-. In ref 3, this curvature difference was ascribed to electrostriction-induced enhancement in the rigidity of the solvent structure near the solute as the solute dipole increases. As a result, the solvent reorganization free energy λ varies with the solute electronic state. In EMI+PF6-, the reorganization free energies defined on the NP and IP curves are, respectively, λNP ) 38 kcal/mol and λIP ) 44 kcal/mol. The corresponding values in acetonitrile are λNP ) 36 kcal/mol and λIP ) 38 kcal/mol. The λIP–λNP difference in EMI+PF6- is consider-

(10)

are also presented, where λav ) (λNP + λIP)/2 is employed as the solvent reorganization free energy. Overall, the Marcus theory describes free energetics of CS/CR in EMI+PF6- reasonably well. Considering dramatic electrostrictive effects in RTILs, this level of agreement is quite remarkable. Nevertheless, the discrepancy between the MD and Marcus theory becomes substantial when ET becomes strongly exo- or endothermic. For instance, the onset of the inverted regime for CS is ∆Frxn ) -44 kcal/ mol, whereas it starts at ∆Frxn ) -38 kcal/mol for CR. Thus, the difference in free energetics between CS and CR in the inverted regime is not negligible, and the Marcus theory with λav fails to capture this. For acetonitrile, we note that eq 10 holds very well, except for highly endoor exothermic cases because its λIP-λNP difference is small. ET Dynamics. We proceed to ET barrier-crossing dynamics. If the magnitude of electronic coupling between the diabatic states is larger than kBT (kB ) Boltzmann’s constant), ET is well-described as activated barrier crossing on a single electronic curve. If solvent relaxation in the reactant and product wells is fast, the barrier crossing is rate-limiting. In this case, the ET rate kET becomes

kET ≈ kb ) κkTST

kTST )

ωs,R exp[-∆Fq ⁄ kBT] (11) 2π

where kb is the barrier crossing rate and ωs,R is the solvent frequency in the reactant well. The transmission coefficient κ measures the deviation of kb induced by solvent dynamics in the barrier region from the transition-state theory (TST) prediction kTST. In the Grote–Hynes (GH) theory,49 where the reactive mode is described via the generalized Langevin equation, the transmission coefficient is given by the self-consistent equation

[

ζ˜(ωbκGH) κGH ) κGH + ωb

]

-1

(12)

where ωb is the barrier frequency, ζ(t) is the time˜ dependent solvent friction in the barrier region, and ζ(ω) is its Laplace transform

ζ˜(ω) )

∫ ∞0 dtζ(t)e-ωt

ζ˜(0) )

∫ ∞0 dtζ(t)

(13)

Thus, barrier-crossing dynamics in the GH theory are governed by the friction at the reactive frequency κGHωb. In the limit of slow barrier crossing, eq 12 reduces to the ˜ Kramers (KR) theory,50 i.e., κKR ) -(ζ(0)/2ω b) + 2 1/2 ˜ ) + 1] , where barrier crossing is determined [(ζ(0)/2ω b ˜ by the total friction ζ(0). Because the determination of ζ(t) in the unstable barrier region is not amenable, we instead use the friction defined in a stable solvent well.51 Results for ζ(t) thus VOL. 40, NO. 11, 2007 / ACCOUNTS OF CHEMICAL RESEARCH

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Various Solution-Phase Processes in RTILs Shim et al.

7. Concluding Remarks

FIGURE 11. (a) Time-dependent friction and (b) transmission coefficient for ET in EMI+PF6- and CH3CN. In b, 2 kcal/mol was employed for electronic coupling between the IP and NP states.

obtained are exhibited in Figure 11a.4 Similar to solvation dynamics in section 3 above, ζ(t) shows bimodal relaxation. The long-time decay of ζ(t) in EMI+PF6- is extremely slow, while its relaxation in acetonitrile is completed in 1–2 ps. Because of a huge memory effect in EMI+PF6-, its total friction is about 50 times higher than ˜ that of acetonitrile. Their respective ζ(0) values are 1300 and 27 ps-1. Despite this startling difference in overall ˜ friction, ζ(ω) values of the two solvents become similar for ω J 10 cm-1. This means that for solvent-collective motions faster than ∼10 cm-1, the properties of dissipative dynamics will be more or less the same between the two solvents! Results for κGH and κKR are compared in Figure 11b.8 We notice that the GH and KR predictions for the ET rate are comparable in acetonitrile. A similar agreement between the two was observed previously in CH3Cl.51 In contrast, the GH and KR results in EMI+PF6- are totally different; κGH is larger than κKR by nearly 2 orders of magnitude! The main reason for this discrepancy is that ˜ the friction relevant to barrier crossing, i.e., ζ(ω) at the reactive frequency κGHωb, is smaller than the total friction ˜ GHωb) ≈ 9 ps-1 by 2 decades. To be specific, ζ(κ -1 ˜ ) 1300 ps-1. Because (κGHωb ≈ 50–100 cm ), while ζ(0) of erroneous inclusion of the large contribution from the ˜ long-time friction, the KR description based on ζ(0) drastically underestimates κ and kET in EMI+PF6-. Thus, it would be totally incorrect to assume that the Kramers theory would apply to RTILs simply because it works well for polar solvents of similar effective polarity. Another important feature is that TST provides a reasonable framework for ET kinetics not only in acetonitrile but also in EMI+PF6-. The kET results with account of barrier-crossing dynamics agree with the TST predictions within a factor of ∼2. Although we do not discuss it here, the inclusion of activation/deactivation dynamics does not affect this state of affairs significantly.8 This could have an important bearing on other systems, e.g., isomerization reactions,52,53 whose kinetics in RTILs were found to be considerably faster than estimated on the basis of viscosity. 1136

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In this Account, we have presented a brief review of our recent efforts to gain a theoretical understanding of solvation and related processes in RTILs. Despite a number of apparent similarities to normal polar solvents, we have found that RTILs are quite unique in many respects in both structure and dynamics. Specifically, the imidazolium-based RTILs studied here show high effective polarity and large electrostriction. Their solvation dynamics span a wide range of differing time scales. Despite their high viscosity, short-time solvation dynamics are in the subpicosecond regime and make a major contribution to the overall relaxation. Their long-time dynamics, on the other hand, are close to a stretched exponential decay. A similar nonexponential behavior is also found in rotational dynamics of small nonpolar solutes. This indicates that RTILs are dynamically heterogeneous. Another interesting finding is that the TST provides a good framework to describe activated ET in RTILs, even though they are much more viscous than normal polar solvents. Thus, continued efforts of both theory and experiments will be definitely worthwhile and desirable to unveil molecular details of a wide range of differing solution-phase processes in RTILs and to elucidate their sometimes intriguing and anomalous behaviors. Many works presented here were supported in part by KOSEF through the National Core Research Center for Systems BioDynamics and by NSF Grant CHE-0098062.

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